Question

Show that 1/(3-√8)  -  1/(√8-√7)  +  1/(√7-√6)  -  1/(√6-√5)  +  1/(√5-2)  =  5

Answer 1

=1/(3-2.828)-1/(2.828-2.645)+1/(2.645-2.449)-1/(2.449-2.236)+1/(2.236-2)
=1/(0.172)-1/(0.183)+1/(0.916)-1/(0.213)+1/(0.236)
=5.813-5-4644+5.1020-4.6948+4.237
=4.99
=5      Approximately

Answer 2

  1/(3-√8) - 1/(√8-√7) + 1/(√7-√6) - 1/(√6-√5) + 1/(√5-2) = 51/(3-rt8)=[1/(3-rt8)]{(3+rt8)/(3+rt8)]  ..... (by rationalising)
           =(3+rt8)/(9-8)       from ...a^2-b@=(a+b)(a-b)
           =3+rt8
as first term all terms will be rationalised...so the expression becomes
     3+rt8-rt8-rt7+rt7+rt6-rt6-rt5+rt5+2
    then all root terms will get cancelled
=3+2=5